Problem: Simplify the following expression: $\sqrt{54}-\sqrt{6}+\sqrt{24}$
First, try to factor any perfect squares out of the radicals. $= \sqrt{54}-\sqrt{6}+\sqrt{24}$ $= \sqrt{9 \cdot 6}-\sqrt{6}+\sqrt{4 \cdot 6}$ Separate the radicals and simplify. $= \sqrt{9} \cdot \sqrt{6}-\sqrt{6}+\sqrt{4} \cdot \sqrt{6}$ $= 3\sqrt{6}-\sqrt{6}+2\sqrt{6}$ Finally, simplify by combining the terms. $= ( 3 - 1 + 2 )\sqrt{6} = 4\sqrt{6}$